Nonlinear dynamics of soft fermion excitations in hot QCD plasma I: Soft-quark–soft-gluon scattering

Within the framework of the hard thermal loop effective theory we derive a system of Boltzmann-like kinetic equations taking into account the simplest processes of nonlinear interaction of soft fermionic and bosonic QCD plasma excitations: elastic scattering of soft-(anti)quark excitations off soft-gluon and soft-quark excitations, pair production of soft quark–antiquark excitations, annihilation into two soft-gluon excitations. The matrix elements of these processes to leading order in the coupling constant g are obtained. The iterative method of calculation of the matrix elements for the higher processes of soft-mode interactions is proposed. The most general expression for the emitted radiant power induced by the effective currents and effective sources in a quark–gluon plasma (QGP) taking into account an existence of fermion sector of plasma excitations is defined. The explicit form of the linearized Boltzmann equation accounting for scattering of color(less) plasminos off color(less) plasmons is written out.